A Comparison of Three Approaches to the Reduced-Scaling Coupled Cluster Treatment of Non-Resonant Molecular Response Properties

We have investigated the performance of the reduced-scaling coupled cluster method based on projected atomic orbitals (PAOs), pair natural orbitals (PNOs), and orbital specific virtuals (OSVs) for the prediction of linear response properties. These methods introduce different degrees of controllable sparsity in the ground-state and perturbed coupled cluster wave functions, leading to localization errors in properties such as dynamic polarizabilities and specific optical rotations. Using a series of chiral test compounds, we find that the inherent costs associated with computing response properties are significantly greater than those for determining the ground-state energy. As the dimensionality of the molecular system increasesfrom (pseudo)­linear structures, such as fluoroalkanes, to cagelike structures, such as β-pinenethe crossover point between canonical-orbital and localized-orbital algorithms increases substantially. Furthermore, both the OSV and PNO methods provide greater reduction in cost (as measured by the size of the double-excitation space) than do PAOs, and PNOs provide the greatest level of sparsity for the systems examined here. Single-excitation truncation induces much larger errors than corresponding doubles truncation due to the fact that the first-order contribution to the one-electron perturbed wave function appears in the singles amplitudes. Both the PNO and OSV methods perform reasonably well for frequency-dependent polarizabilities provided appropriate thresholds are used for the occupation-number and weak-pair cutoffs on which each method depends. Specific rotations, however, are very sensitive to wave function truncation, to the extent that aggressive thresholds can yield the incorrect sign of the rotation, due to the delicate balance of positive and negative wave function contributions to the mixed electric-/magnetic-field response.